Math Pacing Graphing Systems of Equations

Many real-world problems can be solved using a system of equations.

Example 1-3a Bicycling Tyler and Pearl went on a 20-kilometer bike ride that lasted 3 hours. Because there were many steep hills on the bike ride, they had to walk for most of the trip. Their walking speed was 4 kilometers per hour. Their riding speed was 12 kilometers per hour. How much time did they spend walking? Words You have information about the amount of time spent riding and walking. You also know the rates and the total distance traveled. Variables Let the number of hours they rode and the number of hours they walked. Write a system of equations to represent the situation. Write & Solve a System of Equations

Example 1-3a Equations The number of hours riding plus the number of hours walking equals the total number of hours of the trip. The distance traveled riding plus the distance traveled walking equals the total distance of the trip. r+w= 3 12r+4w4w= 20 Write & Solve a System of Equations

Example 1-3a Graph the equationsand. The graphs appear to intersect at the point with the coordinates (1, 2). Check this estimate by replacing r with 1 and w with 2 in each equation. Write & Solve a System of Equations

Example 1-3a Check Answer: Tyler and Pearl walked for 3 hours. Write & Solve a System of Equations

Example 1-3b Alex and Amber are both saving money for a summer vacation. Alex has already saved $100 and plans to save $25 per week until the trip. Amber has $75 and plans to save $30 per week. In how many weeks will Alex and Amber have the same amount of money? Answer: 5 weeks number of weeks amount of money saved Write & Solve a System of Equations